Introduction:
Local shear failure is a type of soil failure that occurs in certain types of soils when subjected to shear stresses. It is associated with soils having high compressibility. This means that soils that exhibit high levels of deformation under applied loads are more prone to local shear failure.

Explanation:
Local shear failure occurs when the shear strength of a soil is exceeded, leading to the development of localized shear zones within the soil mass. This failure mechanism is typically observed in soils that have certain characteristics, such as high compressibility. Here is a detailed explanation of why high compressibility is associated with local shear failure:

1. High compressibility:
Soils with high compressibility have the ability to undergo large deformations under applied loads. This characteristic is often associated with low-strength soils, such as silts and clays, which have high water content and fine-grained particles. The high compressibility of these soils makes them more susceptible to local shear failure.

2. Shear strength:
Shear strength is a measure of a soil's resistance to deformation under shear stresses. It depends on several factors, including the soil's composition, density, and water content. Soils with high compressibility often have low shear strength, making them more prone to local shear failure.

3. Stress distribution:
During loading, stress is transferred from the applied load to the soil. In soils with high compressibility, the stress distribution is often non-uniform, resulting in localized areas of high stress concentration. These areas are more likely to exceed the shear strength of the soil, leading to the initiation of local shear failure.

4. Deformation patterns:
Soils with high compressibility tend to undergo large deformations, which can result in the development of shear planes or zones within the soil mass. These localized shear zones can propagate and lead to the failure of the entire soil mass.

Conclusion:
In summary, local shear failure is associated with soils having high compressibility. Soils with high compressibility exhibit large deformations under applied loads, have low shear strength, and are prone to the development of localized shear zones. Understanding these characteristics is crucial in engineering practices to avoid potential failures and ensure the stability of structures built on such soils.